Question

In Mohr's circle for plane stress, what do the points on the circle represent?

• A. Principal stresses and their directions
• B. Shear stresses only
• C. Normal stresses only
• D. Strain energy values

Hint:

Mohr's circle is a complete graphical tool for stress state analysis.
It links normal stresses, shear stresses, and plane orientations, with its principal focus on finding the principal stresses and their directions.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to identify what the coordinate points plotted on a Mohr's circle of stress represent.

Step 2: Key Formula or Approach: This is a standard graphical concept in solid mechanics. Mohr's circle is used to visualize stress transformations and determine principal stresses, maximum shear stress, and the orientation of the planes on which they act.

Step 3: Detailed Explanation:

• Mohr's circle coordinates represent normal stress (\(\sigma\)) on the horizontal axis and shear stress (\(\tau\)) on the vertical axis.

• Every point on the boundary of the circle corresponds to the state of stress acting on a plane with a specific angular orientation.

• Specifically, the two points where the circle intersects the horizontal axis (\(\tau = 0\)) represent the maximum and minimum principal stresses.

• The angle of rotation around the center of the circle represents twice the physical angle of the plane, allowing engineers to identify the directions of the principal planes.

• Therefore, the geometric properties of Mohr's circle represent both the magnitudes of the principal stresses and their spatial directions.

Step 4: Final Answer:
The points on Mohr's circle represent the principal stresses and their directions.